1. Field of the Invention
This invention relates generally to moving structures and more particularly, to vibratory rate gyroscopes. This invention may be used to reduce error caused by imperfections in implementation of such structures.
2. Description of the Related Art
Rate gyroscopes are sensors that measure rotation rate. Rate gyroscopes have uses in many commercial and military applications including, but not limited to, inertial navigation, vehicular skid control, and platform stabilization.
A vibratory rate gyroscope is a sensor that responds to a rotation rate by generating and measuring Coriolis acceleration. Coriolis acceleration is generated by an object, such as a proof-mass, that has some velocity relative to a rotating reference frame. In vibratory rate gyroscopes, one or more proof-masses are often suspended from flexures and made to oscillate thus providing a velocity necessary to generate Coriolis acceleration. Measurement of the resulting Coriolis acceleration can then yield an estimate of the rotation rate of the sensor.
An idealized version of a single-mass sensor is shown in FIG. 1. In this figure a three-dimensional, mutually orthogonal coordinate system is shown for reference. The axes are arbitrarily labeled “X”, “Y”, and “Z” to enable description of background material as well as the invention. Oscillation that is largely coincident with the X-axis is often referred to as the drive-mode or driven-mode. Coriolis acceleration is generated perpendicular to the drive-mode along the sense-mode, which lies largely along the Y-axis. The Coriolis acceleration generated by the system shown in FIG. 1 is given by:αCoriolis=2ΩzDxωxcos(ωxt)  Equation 1where aCoriolis is the Coriolis acceleration generated along the sense-mode, Ωz is the rotation rate to be measured about the Z-axis, and ωx and Dx are the frequency and magnitude of drive-mode oscillation, respectively. The Coriolis acceleration causes an oscillatory displacement of the sensor along the sense-mode with magnitude proportional to the generated Coriolis acceleration. Ideally, the drive-mode is coincident with the forcing means used to sustain oscillation (located along the X-axis or drive-axis), and the sense-mode is coincident with the sensing means used to detect displacements due to Coriolis acceleration (located along the Y-axis or sense-axis).
The simplified schematic of FIG. 1 shows proof-mass 52, attached to substrate 51 via a compliant suspension that may be modeled by two springs 50a, and 50b. Typically the compliant suspension is designed such that the suspension may be modeled by an orthogonal decomposition into two springs: spring 50b lying along the sense-mode and spring 50a lying along the drive-mode. Mathematically this translates into a goal of being able to decompose the suspension into a diagonal spring matrix when an orthogonal coordinate system comprising the sense-axis and the drive-axis is chosen. The design and fabrication of the proof-mass and the suspension will dictate the actual orientation of the drive- and sense-modes with respect to the driving and sensing axes. Often, the suspension may have small, off-diagonal spring-matrix components due to, for example, processing imperfections during a reactive-ion-etching step, or misalignment of the drive and sense-axes to their corresponding modes.
FIG. 2 shows a simplified schematic of a dual-mass gyroscope. In a dual-mass gyroscope, a differential oscillation of proof-masses 62a and 62b along the drive-mode lead to a differential Coriolis-acceleration induced oscillation along the sense-mode. The suspension of a dual mass gyroscope may be modeled by springs 60a, 60b, and 60c. Often the suspension may be further decomposed to have additional springs (not shown) that provide restoration of common-mode deflections along the X-axis. The operation of dual-mass gyroscopes is well known by those skilled in the art, with example dual-mass gyroscopes described in Clark et al. U.S. patent application Ser. 09/321,972 filed May 28, 1999; Geen, U.S. Pat. No. 5,635,640, Issued Jun. 3, 1997; Geen, U.S. Pat. No. 5,635,638, Issued Jun. 3, 1997; Ward et al., U.S. Pat. No. 5,747,961, Issued May 5, 1998; Lee et al., U.S. Pat. No. 5,757,103, Issued May 26, 1998.
It is important to understand that the Coriolis acceleration signal along the sense-axis is in phase with velocity of the drive-mode, which is 90 degrees out-of-phase with proof-mass displacement along the drive-mode. While the Coriolis acceleration is 90 degrees out-of-phase with the proof-mass displacement along the drive-mode, displacements along the sense-mode due to Coriolis acceleration may have a different phase relationship to the proof-mass displacement along the drive-mode depending on several factors including: the relative values of drive-mode oscillation frequency to sense-mode resonant frequency, and the quality factor of the sense-mode.
Forces are often applied to vibratory-rate gyroscopes to generate or sustain proof-mass oscillation. Forces may be applied to the gyroscope using variable air-gap capacitors formed between one or more plates or conductive nodes attached to the proof-mass and one or more plates or conductive nodes attached to the substrate. Note that electrostatic forces result between charged capacitor plates. The magnitude and direction of the force is given by the gradient of the potential energy function for the capacitor as shown below.
                              F          _                =                              -                          ∇              U                                =                      -                          ∇                              [                                                      Q                    2                                                        2                    ⁢                                          C                      ⁡                                              (                                                  x                          ,                          y                          ,                          z                                                )                                                                                            ]                                                                        Equation        ⁢                                  ⁢        2            
As an example, an appropriate oscillation in the gyroscope may be generated using a force along a single axis (e.g. the X-axis). Equation 2 implies that any capacitor that varies with displacement along the X-axis will generate an appropriate force. An implementation of a pair of such capacitors is shown in FIG. 3. This capacitor configuration has a number of advantages including ample room for large displacements along the X-axis without collisions between comb fingers. By applying differential voltages with a common mode bias VDC across electrically conductive comb fingers 72a, 73a and 72b, 73b a force that is independent of X-axis displacement and linear with control voltage, vx is created.
                                          V            1                    =                                    V              DC                        -                          v              x                                      ⁢                                  ⁢                              V            2                    =                                    V              DC                        +                          v              x                                      ⁢                                  ⁢                              F            x                    =                                                                      1                  2                                ⁢                                                      ∂                    C                                                        ∂                    x                                                  ⁢                                  V                  2                  2                                            -                                                1                  2                                ⁢                                                      ∂                    C                                                        ∂                    x                                                  ⁢                                  V                  1                  2                                                      =                          2              ⁢                                                C                  0                                                  X                  0                                            ⁢                              V                DC                            ⁢                              v                x                                                                        Equation        ⁢                                  ⁢        3            where C0 and X0 are the capacitance and X-axis air-gap at zero displacement respectively. An equivalent method of applying forces chooses V1, V2 such that:V1=VDC−νx V2=−VDC−νx  Equation 4
Note that in both of these cases the magnitude of the force is proportional to the control voltage, vx, and the DC bias voltage, VDC. This permits the magnitude and direction of the force to be directly controlled by varying either vx or VDC while maintaining the other voltage constant. Other prior-art work has used parallel-plate capacitors, or piezoelectric transduction elements to effect motion.
Many methods are known that sense motion or displacement using air-gap capacitors. Details of capacitive measurement techniques are well known by those skilled in the art. These methods may be used for detection of displacement due to Coriolis acceleration, measuring quadrature error (described below), or as part of an oscillation-sustaining loop. Often a changing voltage is applied to two nominally equal-sized capacitors, formed by a plurality of conductive fingers, with values that change in opposite directions in response to a displacement. For example, one method applies voltages to these sensing capacitors in a manner that generates a charge that is measured by a sense interface (see for example: Boser, B. E., Howe, R. T., “Surface micromachined accelerometers,” IEEE Journal of Solid-State Circuits, vol. 31, pp. 366–75, March 1996., or Lemkin, M., Boser B. E., “A micromachined fully differential lateral accelerometer,” CICC Dig. Tech. Papers, May 1996, pp. 315–318.). Another method uses a constant DC bias voltage applied across two sensing capacitors. Any change in the capacitance values results in current flow that is detected by a sense interface (See for example: Clark, W. A., Micromachined Vibratory Rate Gyroscopes, Doctoral Dissertation, University of California, 1997; Roessig, T. A., Integrated MEMS Tuning Fork Oscillators for Sensor Applications, University of California, 1998; Nguyen, C. T.-C., Howe, R. T., “An integrated CMOS micromechanical resonator high-Q oscillator,” IEEE JSSC, pp. 440–455, April 1999). Furthermore, some methods of capacitive detection use time-multiplexing (See for example: M. Lemkin, B. E. Boser, “A three-axis micromachined accelerometer with a CMOS position-sense interface and digital offset-trim electronics,” IEEE Journal of Solid-State Circuits, pp. 456–68, April 1999) or frequency multiplexing (See for example Sherman, S. J, et. al., “A low cost monolithic accelerometer; product/technology update,” International Electron Devices Meeting, San Francisco, Calif., December 1992, pp. 501–4) to enable electrostatic forces to be applied to a microstructure and displacement or motion of the microstructure to be sensed using a single set of capacitors. An example of an application in which time- or frequency-multiplexing of capacitor function in such a manner may prove useful includes a force-feedback loop.
Provided with a controllable force applied to a structure and a measure of the structure's deflection, the structure may be driven into oscillation using feedback. Oscillation is achieved by measuring the structure's displacement or velocity then determining the magnitude, and/or phase of the force or forces to apply to the structure. The measurement of the structure's displacement and the force(s) applied may be electrostatic as described above. In a dual-mass gyroscope the position or velocity detected by the sense interface often reflects relative motion between the two masses, and the forces applied to the two masses may contain a differential force component. Many methods that sustain drive-mode oscillation are known by those skilled in the art. Descriptions of oscillation-sustaining circuits and techniques may be found in, for example (Roessig, T. A., Integrated MEMS Tuning Fork Oscillators for Sensor Applications, University of California, 1998; Nguyen, C. T.-C., Howe, R. T., “An integrated CMOS micromechanical resonator high-Q oscillator,” IEEE JSSC, pp. 440–455, April 1999; Lemkin, et al. U.S. patent application Ser. No. 09/322,840 Filed May 28, 1999; Putty et al., U.S. Pat. No. 5,383,362, Issued Jan. 24, 1995; Ward, U.S. Pat. No. 5,600,064, Issued Feb. 4, 1997). Note that driven-mode oscillations may also be excited open loop, see for example Geiger, W. et al. “A mechanically controlled oscillator,” Transducers 99, Sendai Japan, Jun. 7–10, 1999 pp. 1406–09.
Because of imperfections introduced in the manufacturing process, the gyroscope driven-mode and sense-axis may not be perfectly orthogonal. Imperfections in elements of the suspension are one possible source of this non-orthogonality. A non-orthogonal relationship between the driven-mode and the sense-axis may cause a sense capacitance change proportional to displacement in the drive-mode to appear along the sense axis. When the sense-capacitance change is detected using a position-sense interface, an output signal substantially in-phase with displacement may result.
This undesirable signal is termed quadrature error. Since Coriolis acceleration is in phase with velocity, these two signals are ideally separated by 90 degrees of phase, hence the name quadrature error. Note, however, the magnitude of the quadrature error may be many orders of magnitude greater than the quantity of interest: Coriolis acceleration.
Due to the similarity and relative magnitude of the two signals, quadrature-error can contaminate if not overwhelm the sensor output. For example, a small amount of phase lag in detection circuitry can lead to quadrature error leakage into the sensor output. Results of this leakage may include large sensor output offsets, output-offset drift, and noise. In addition, large quadrature-error signals may cause saturation of sense-mode interfaces. Quadrature-error has been addressed in different ways in prior art gyroscopes including forcing mechanisms (Ward, U.S. Pat. No. 5,600,064, Issued Feb. 4, 1997; Clark et al, U.S. Pat. No. 5,992,233, Issued Nov. 30, 1999; Clark et al., U.S. patent application Ser. No. 09/321,972, Filed May 28, 1999) and carefully-designed, well-controlled fabrication of mechanical structures (Geen, J. “A path to low cost gyroscopy,” IEEE Solid-State Sensor and Actuator Workshop, Hilton Head Island, S.C., Jun. 8–11, 1998, pp 51–4.). A good description of sources of quadrature-error and the effect on vibratory-rate gyroscopes may be found in Clark, W. A., Micromachined Vibratory Rate Gyroscopes, Doctoral Dissertation, University of California, 1997.